Fluidic function generator

ABSTRACT

A FLUIDIC BRIDGE CIRCUIT CONSISTING OF A PAIR OF FIXED RESTRICTORS AND A PAIR OF VARIABLE RESTRICTORS GENERATES A FLUID SIGNAL WHOSE PRESSURE VARIES IN A PREDETERMINED NONLINEAR MANNER. THE VARIABLE RESTRICTORS ARE FORMED BY AN AXIAL GROOVE IN A ROTARY SHAFT AND A VENTED GROOVE FORMED IN ACCORDANCE WITH A PREDETERMINED NONLINEAR MATHEMATICAL FUNCTION IN A SLEEVE MEMBER SURROUNDING THE SHAFT. THE VENTED POINT OF OVERLAP OF THE NONLINEAR GROOVE WITH RESPECT TO THE SHAFT AXIAL GROOVE DIVIDES THE AXIAL GROOVE INTO THE TWO VARIABLE RESTRICTORS. PRESSURIZED FLUID IS SUPPLIED TO THE JUNCTURE OF THE FIXED RESTRICTORS, AND THE FLUID PRESSURE AT THE JUNCTURE OF EACH FIXED AND VARIABLE RESTRICTOR VARIES NONLINEARLY WITH CHANGE IN SHAFT ANGULAR POSITION IN ACCORDANCE WITH THE PREDETERMINED NONLINEAR FUNCTION.

Nov 2, 1971 HONDA 3,616,816

FLUIDIC FUNCTION GENERATOR Filed June 1, 1970 [77 Van g; Thomas 5.Hana/a,

by Q

3,616,816 FLUIDIC FUNCTION GENERATOR Thomas S. Honda, Scotia, N.Y.,assignor to General Electric Company Filed June 1, 1970, Ser. No. 42,224Int. Cl. F15c 3/02; F16k 11/14 US. Cl. 137-609 10 Claims ABSTRACT OF THEDISCLOSURE A fluidic bridge circuit consisting of a pair of fixedrestrictors and a pair of variable restrictors generates a fluid signalwhose pressure varies in a predetermined nonlinear manner. The variablerestrictors are formed by an axial groove in a rotary shaft and a ventedgroove formed in accordance with a predetermined nonlinear mathematicalfunction in a sleeve member surrounding the shaft. The vented point ofoverlap of the nonlinear groove with respect to the shaft axial groovedivides the axial groove into the two variable restrictors. Pressurizedfluid is supplied to the juncture of the fixed restrictors, and thefluid pressure at the juncture of each fixed and variable restrictorvaries nonlinearly with change in shaft angular position in accordancewith the predetermined nonlinear function.

My invention relates to a fluidic device for generating a pressuresignal varying in a predetermined nonlinear manner, and in particular,to a device for generatnig such pressure signals as a nonlinear functionof the angular position of a rotary shaft.

This application is related to a concurrently filed patent applicationS.N. 42,292, entitled Fluidic Angular Position Sensor having the sameinventor and assigned to the same assi-gnee as the present invention.

In many control systems, specific nonlinear mathematical functions mustbe generated in order to accomplish a particular control action,examples of such functions being the sine or cosine of an angleparameter in the control system and the square or square root of aparticular scaler quantity. Thus, in an attitude control, it is oftennecessary to transform signals according to the sine and cosine functionof a relative gimbal angle. In the particular field of fluidic controlsystems, resolvers and other type fluidic function generators of highaccuracy are not presently known and are a necessary component in orderto obtain all fluidic control systems. The prior art function generatorsand resolvers are primarily electronic, mechanical or electromechanical,and thus their use in fluidic control systems necessitates theadditional use of suitable transducers for converting the signals to theproper form.

Therefore, one of the principal objects of my invention is to provide afluidic function generator and fluidic resolver.

Another object of my invention is to provide the device with an improvedaccuracy due to a relatively large range of motion of the elements ofthe device.

Briefly stated, my fluidic function generator device includes a rotaryshaft and a sleeve member supported in a housing. The rotary shaft isprovided with an axial groove and is rotatable relative to the sleevemember. The sleeve member surrounds a portion of the shaft including themajor portion of the axial groove in fluid-tight relationship and isprovided with a vented groove formed in accordance with a predeterminednonlinear mathematical function in overlapping fluid communication withthe axial groove. Pressure signals representing the nonlinear functionare developed at the output of a fluidic bridge circuit consisting of apair of fixed restrictors and a pair of variable restrictors. The ventedpoint of overlap of the non- "United States Patent 3,616,816 PatentedNov. 2., 1971 "ice linear groove with the shaft axial groove divides theaxial groove into the two variable restrictors. Pressurized fluid issupplied to a juncture of the fixed restrictors, and the differentialpressure at the two junctures of the fixed and variable restrictorsvaries nonlinearly with change in shaft angular position in accordancewith the predetermined nonlinear function.

The features of my invention which I desire to protect herein arepointed out with particularity in the appended claims. The inventionitself, however, both as to its organization and method of operation,together with further objects and advantages thereof, may best beunderstood by reference to the following description taken in connectionwith the accompanying drawing wherein like parts in each of the severalfigures are identified by the same reference character, and wherein:

FIG. 1 is a diagrammatic view of a fluidic function generatorconstructed in accordance with my invention and capable of developing asignal which varies as the square of the shaft input angle;

FIG. 2 is a diagrammatic view of a fluidic resolver device capable ofgenerating the sine or cosine function; and

FIG. 3 is a perspective sectional view taken along line 3-3 in FIG. 2illustrating the vented groove formed only on the inside surface of thesleeve member.

Referring now in particular to FIG. 1, there is shown a cylindricalrotary shaft 4 and a circular sleeve member 5 both supported in ahousing shown by the cross-hatching and identified as a whole by numeral6. Shaft 4 is rotatable relative to sleeve member 5 but is influid-tight relationship therewith, the fluid-tightness being obtainedby any conventional means such as capillary clearance. The drivenportion4a of rotary shaft 4 extends outward of the housing, shown extending tothe left of the housing, and the shaft is mounted in conventional thrustand journal bearings 7 and 8 for support within the housing. An axialgroove 9 having constant narrow width and depth dimensions is formedinto the outer surface of shaft 4 along the entire length of the centralportion thereof. Shaft 4 has reduced diameter portions 4b intermediatebearings 8 and the shaft central portion to form two annular shapedchambers 10 in the volumes not occupied by the reduced diameter portions412 of the shaft. A pair of first fluid flow passage 11 and 12 havefirst ends thereof in fluid communication with chambers 10 and secondends thereof comprise the outputs of my fluidic function generatordevice across which is developed a differential pressure P P A pair ofsecond fluid flow passages 13 and 14 have first ends thereof in fluidcommunication with passages 11 and 12 and second ends thereof in fluidcommunication with a source of pressurized fluid P at the juncture ofpassages 13 and 14. The fluid utilized in my device may be a gas such aspressurized air, or a liquid such as pressurized oil, that is, my devicecan be pneumatic or hydraulic. Passages 13 and 14 are provided withfixed fluid flow restrictors 15 and 16', respectively. In general,restrictors 15 and 16 have equal flow restrictive values. Sleeve member5 is concentric with shaft 4 and surrounds the central portion thereof.The ends of sleeve member 5 are in close proximity to the ends of thecentral portion of shaft 4, being spaced therefrom by the housingmembers 6a which support the ends of the sleeve member within thehousing. Sleeve member 5 is provided with a vented groove ofpredetermined nonlinear shape which is adapted to be in overlappingfluid com munication with the axial groove 9 on rotary shaft 4. Theparticular shape of groove 17 determines the particular mathematicalfunction to be generated by my device. Groove 17 may be vented to theatmosphere surrounding the housing by being formed completely throughthe side of sleeve member 5 as shown in FIG. 1, or alternatively, may beformed on the inner surface of the sleeve member in a manner similar tothat depicted in a sectional view in FIG. 3 for a resolver device. Theangular extension of groove 17 around sleeve member 5 is dependent uponthe particular mathematical function to be generated. Thus, in thespecific fluidic function generator device depicted in FIG. 1 forgenerating a mathematical square function, groove 17 extends less than360 around sleeve member 5 in the predetermined nonlinear patternnecessary to generate an output differential pressure representing thesquare of the shaft angular displacement input P P =k() where 0 is theshaft angular displacement from a zero reference angle and k is the gainof the device. The shape of groove 17 for describing the mathematicalsquare function is as follows. The starting point of the groove 17 ismidway along the length of sleeve member 5 corresponding to the midpointof axial groove 9. Groove 17 is then formed in sleeve member 5 inaccordance with the square function, that is, the unidirectional axialdisplacement described by the groove for equal increments of angulardisplacement of the sleeve member varies nonlinearly from near zero forthe smallest angular displacement to a relatively large andpredetermined value for the larger angular displacement which is lessthan 360 from the starting point angular position. It should be obviousthat the square root, cube, and other nonlinear function can be readilyachieved by proper shaping of groove 17.

As stated hereinabove, axial groove 9 has a width and depth of narrowdimensions such that it presents a relatively high restriction to fluidflow therethrough. Groove 17 is of significantly larger depth, and, orwidth dimensions such that it prevents a negligible restriction to thefluid being vented therethrough. Thus, it can be appreciated that myfiuidic function generator device forms a fluidic bridge circuitincluding a pair of fixed restrictors and 16 and a pair of variablerestrictors formed by the axial groove 9 divided into two variablelength parts defined between the ends thereof and the vented point ofoverlap 19 with groove 17. Thus, in the particular angular position 0 ofshaft 4 in FIG. 1, the first of the two variable restrictors 9a isdefined by the length of the axial groove between the left end thereofand the point of overlap 19 with the vented groove 17, and the secondvariable restrictor 9b is the length of axial groove 9' defined betweenoverlap point 19 and the right end of the axial groove. The fiuidicbridge circuit is thus completely described as including a pair of fixedrestrictors 15, 16, a pair of variable restrictors 9a, 9b, a source ofpressurized fluid supplied to the juncture of fixed restrictors 15- and16, and a vent at the juncture 19 of the variable restrictors 9a and917.

It is evident that the point of overlap 19 (i.e., the juncture ofvariable restrictors 9a and 9b) (shifts longitudinally) along the axialgroove 9 with rotation of shaft 4, and in particular, varies nonlinearlywith changes in angular position or angular displacement from aparticular shaft 4 reference angular position, that is, the point ofoverlap 19 shifts axially in unequal increments for equal increments inangular displacement of shaft 4. The reference (or zero) position may bechosen at any particular angle orientation of shaft 4, but wouldcommonly be at the orientation wherein axial groove 9 is overlapped by apoint of the nonlinear groove 17 corresponding to zero angle of shaft 4,it being understood that in this first application, sleeve member 5 ismaintained in a fixed position and only shaft 4 is movable relativethereto. It is apparent that the differential pressure P -P developedacross the output ends of passages 11 and 12 is directly proportional toa predetermined nonlinear function of the angular displacement of therotary shaft 4 from its reference position in accordance with theparticular mathematical function described by groove 17 since theangular displacement determines the point of overlap 19 and thus therespective values of variable restrictors 9a and 9b. This differentialoutput pressure varies nonlinearly with changes in the angulardisplacement of the shaft and it can be appreciated that the accuracy ofmy device can be improved by increasing the length of both the axialshaft groove 9 and nonlinear groove 17, or by increasing the diametersof shaft 4 and sleeve member 5 to obtain an even greater length oftravel for a particular rotation of shaft 4. The accuracy of my deviceis also a function of the accuracy with which groove 17 can be formed onthe sleeve member. In the case of the reference position correspondingto one end of groove 17 being located at the midpoint along groove 9,and the groove 17 being displaced from the center of axial groove 9 inonly one direction as in the case of the square function depicted inFIG. 1, the output differential pressure F -P maintains the samepolarity over the entire (less than 360) range of angular displacementof shaft 4. However, in the case of groove 17 being distributed on bothsides of the midpoint of axial groove 9, as in the case of the geometricsine and cosine functions in FIG. 2, the output differential pressurechanges in polarity as the vented overlapped point 19 passes from oneside of the midpoint of axial groove 9 to the other.

Sleeve member 5 has been described hereinabove as being supported in afixed (nonrotary) position within housing 6 of my device. There areapplications, however, wherein relative motion between two rotatablemembers occurs, and it is desired to sense the relative motion inputs.In such case sleeve member 5 is not retained in a fixed nonrotaryposition but is adapted for rotary motion by any suitable means such asthe depicted gear 18 mounted around a central portion of sleeve member 5in FIG. 1. The gear teeth are not illustrated in order to more clearlydepict the shape of groove 17, but they would be parallel to thecoincident axis of shaft 4 and sleeve member 5. In the case wherein themeans for rotating sleeve member 5 is a gear, a second gear (not shown)is positioned in meshing engagement with gear 18 and such second gear issuitably driven by an actuator device such as a motor. In this casewherein both shaft 4 and sleeve member 5 are rotated by independentmeans, the differential pressure P P 'developed across the output endsof passages 11 and 12 is related to the relative motion inputs to shaft4 and sleeve member 5 in accordance with the particular nonlinearmathematical function described by groove 17.

Groove 17 as depicted in FIG. 1 is formed completely through the sideof. sleeve member 5. Alternatively, as depicted in FIG. 2 and thesectional view thereof in FIG. 3, groove 17 is formed in the innersurface of sleeve member 5 and does not pass completely through the sidethereof as in the case of FIG. 1. Suitable venting to the atmosphere isprovided by one or preferably more than one vent holes 30 passingradially outward of groove 17 to the outer surface of sleeve member 5.Groove 17 in the FIG. 1 embodiment may also be formed only in the innersurface of sleeve member 5, and suitably vented, rather than beingformed completely through the sleeve member.

The operation of the FIG. l embodiment of my fluidic function generator(with sleeve member 5 fixed) may be described as follows. At initialsteady state conditions, the vented point of overlap 91 of groove 17relative to axial groove 9 is midway along the axial groove such asvariable restrictors 9a and 9b are equal, that is, the vented point ofoverlap coincides with a zero value 6 of the angular position of shaft4. At this initial or reference condition of shaft 4 relative to sleevemember 5, output pressures P =P A change in angular displace ment ofshaft 4, such as by rotation through an angle 0 from the reference orzero angle results in the vented point of overlap 19 being shiftedaxially to the left of the midpoint as shown in FIG. 1 whereby variablerestrictors 9a or 9b are unequal and result in a particular differentialpressure Pol-"P02 not equal to zero developed across the output ends ofpassages 11* and 12. A further in.-

crease in the angular displacement of shaft 4 results in a greaterdifferential pressure developed across the output in passages 11 and 12in accordance with the mathematical square function. Likewise, asubsequent decrease in the angular displacement of shaft 4 would resultin a smaller differential pressure.

In the case wherein there is relative motion between two rotary members,the output differential represents the square of the relativedisplacement or motion inputs of the two rotary members P P =k( 0 where0 is the angular displacement of the other rotary member, assuming aunity gear ratio, and k is a gain factor for the device.

FIG. 2 illustrates my fluidic function generator operable as a resolverin that it generates the geometric sine or cosine functions. Theelements of the FIG. 2 embodiment may be identical to that in FIG. 1except for the groove 17' formed in sleeve member 5. The shape of groove17' necessary to describe the geometric sine and cosine functions iscircular when viewed from the side as illustrated in FIG. 2 and whenviewed from the end of sleeve member 5. When taken along a plane 45relative to the (longitudinal) axis of sleeve member 5, groove 17 has ashape of an ellipse. Groove 17' thus describes a 360 path around sleevemember and in view of such groove orientation, it is desirable to formsuch groove into the inner surface of sleeve member 5 and not completelythrough the sleeve member as in the case of the square functionillustrated in FIG. 1 which would result in the sleeve member beingsplit into two parts. The perspective sectional view in FIG. 3illustrates one half of groove 17' as would be seen in the plane takenalong line 3-3 in FIG. 2. Suitable means for venting groove 17' to theatmosphere surrounding sleeve member '5 must be provided and for suchpurposes a plurality of vent holes 30 oriented at 90 intervals aroundsleeve member 5 are formed radially from the groove to the outer surfaceof the sleeve member. The outer edges of groove 17' at the inner surfaceof sleeve member 5 are indicated by numerals 31 and the inner edges ofthe groove at the surface parallel to the inner and outer surfaces ofsleeve member 5 and intermediate thereof are designated by numerals 32.

The geometric sine function is obtained by establishing the referenceorientation (i.e., zero angle) of axial groove 9 and groove 17' suchthat the vented point of overlap 19 thereof occurs at the midpoint ofaxial groove 9 such that restrictors 9a and 9b are equal. This wouldcorrespond to overlap point 19 being the top or bottom of groove 17' asviewed in FIG. 2. The particular point of overlap 19 illustrated in FIG.2 is representative of the sine of 90 and 270. Thus, it is evident thatat the zero reference angular position of shaft 4 with respect to sleevemember 5, output pressures P and P are equal and represent the sine of 0or 180. Assuming the zero reference angle to be at the top of groove 17'as viewed in FIG. 2, it is noted that angular displacement of shaft 4through an angle of 90 in the direction wherein overlap point 19 shiftsto the right of the midpoint of axial groove *9 results in the outputdifferential pressure P -P increasing from zero to its maximum value atthe 90 point. Further angular displacement of shaft 4 of an additional90 results in the output differential pressure being reduced to zerocorresponding to the 180 point. An additional angular displacement of 90in the same direction causes a reversal in sign of the outputdifferential pressure which again increases to its maximum value at the270 point and then reduces to zero for an additional 90 displacement,ending up at the starting point and satisfying the identity sine O=sine360=0.

The function generator in FIG. 2 operates as a geometric cosinegenerator by establishing the Zero reference angle at an orientation ofthe axial groove 9 and groove 17' such that the point of overlap is atthe extreme left or right of groove 17 as viewed in FIG. 2.

Thus, as depicted in FIG. 2, the point of overlap 19 at the extreme leftof groove 17 represents the cosine of 0 or 180. Assuming such referenceposition establishes the cosine of 0, the output differential pressure P-P is a maximum due to the maximum unbalance of variable restrictors 9aand 9b. Angular displacement of shaft 4 through obtains a zero outputdifferential pressure due to restrictors 9a and 9b being equal at suchpoint of overlap. A further angular displacement of shaft 4 in the samedirection results in the point of overlap shifting to the extreme rightof groove 17 as viewed in FIG. 2 thereby establishing a maximum outputdifferential pressure of opposite polarity from that occurring with thepoint of overlap at the extreme left of groove 17'. Further, angulardisplacement of shaft 4 results in the output differential pressureassuming values which represent the cosine of angles between and 360 andit is noted that the zero degree point is in correspondence to the 360point as in the case of the sine function.

From the foregoing description, it is apparent that my invention attainsthe objectives set forth and makes available a new fluidic functiongenerator having a high degree of accuracy over its entire range ofoperation. The range of motion of the function generator may beincreased, as desired, by lengthening the axial groove 9 and the groove17 in the sleeve member for certain mathematical functions (i.e., thesquare or square root functions), and by increasing the diameter ofshaft 4 and correspondingly increasing the diameter of sleeve member 5for all mathematical functions including the geometric functions. Thus,the accuracy of my fluidic function generator can be controlled to anydesired degree.

What I claim as new and desire to secure by Letters Patent of the UnitedStates is:

1. A fluidic function generator comprising:

a rotary shaft having an axial groove in the outer surface thereof,

means surrounding a portion of said shaft including the axial groove influid-tight relationship and having a vented groove of predeterminednonlinear shape corresponding to a particular nonlinear mathematicalfunction in overlapping fluid communication with the axial groove, saidshaft being rotatable relative to said nonlinear groove means,

first passage means including a pair of fixed fluid flow restrictorstherein for forming one-half of a fluidic bridge circuit, first ends ofsaid fixed restrictors connected at a juncture supplied from a source ofpressurized fluid, and

second passage means interconnecting nonjuncture second ends of saidfixed restrictors with the two ends of the axial groove on said rotaryshaft for performing the second half of the fluidic bridge circuitconsisting of a pair of variable fluid flow restrictors formed by theaxial groove divided into two variable length parts defined between theends thereof and the vented point of overlap thereof with the nonlineargroove wherein the point of overlap varies nonlinearly with change inangular position of the rotary shaft in accordance with the particularnonlinear mathematical function.

2. The fluidic function generators set forth in claim 1 and furthercomprising:

a housing for supporting said rotary shaft and nonlinear groove means,said nonlinear groove means provided with means for rotary motionrelative to said rotary shaft,

said second passage means having first ends in fluid communication withthe two ends of the axial groove and second ends comprising the outputof said bridge circuit across which is developed a differential pressurethat varies nonlinearly with change in relative angular displacementbetween said rotary shaft and said nonlinear groove means.

3. The fluidic function generator set forth in claim ll wherein:

said nonlinear groove means comprises a sleeve member concentric withsaid rotary shaft and surrounding a. portion of said rotary shaftincluding the major part of the axial groove,

the vented nonlinear groove consisting of a groove formed completelythrough the side of said sleeve member.

4. The fluidic function generator set forth in claim 1 wherein:

said first and second passage means comprise first and second pairs offluid flow passages, respectively,

5. The fluidic function generator set forth in claim 1 and furthercomprising:

a housing for supporting said rotary shaft and nonlinear groove means,said nonlinear groove means being retained within said housing in afixed position,

said second passage means having first ends in fluid communication withthe two ends of the axial groove and second ends comprising the outputof said bridge circuit across which is developed a differential pressurethat varies nonlinearly with change in angular displacement of therotary shaft from a reference angular position in accordance with theparticular nonlinear mathematical function.

6. The fluidic function generator set forth in claim 5 wherein:

said first passage means having first ends in fluid communication withthe juncture supplied from the source of pressurized fluid,

the source of pressurized fluid being maintained at a relativelyconstant pressure,

said first passage means having second ends in fluid communication withsaid second passage means intermediate the ends thereof, and

said rotary shaft provided with reduced diameter portions adjacent bothsides of the shaft portion including the axial groove, the reduceddiameter shaft portions forming annular shaped chambers for providingfluid communication between the ends of the axial groove and the firstends of said second passage means.

7. The fluidic function generator set forth in claim 5 wherein:

said nonlinear groove is formed in accordance with a mathematical squarefunction whereby the differential pressure varies nonlinearly withchange in shaft angular displacement as the square thereof.

8. The fluidic function generator set forth in claim 5 wherein:

said nonlinear groove means comprises a sleeve member concentric withsaid rotary shaft and surrounding a portion of said rotary shaftincluding the major part of the axial groove, the nonlinear groove beingof circular shape when viewed from the side or end of said sleevemember, and being of elliptical shape when viewed in a plane 45 relativeto the axis of said rotary shaft and sleeve member whereby thedifferential pressure varies nonlinearly with change in angulardisplacement of the rotary shaft from a reference angular position inaccordance with the geometric sine or cosine function. 9. The fluidicfunction generator set forth in claim 1 wherein:

said nonlinear groove means comprises a sleeve mem ber concentric withsaid rotary shaft and surrounding a portion of said rotary shaftincluding the major part of the axial groove, the vented nonlineargroove consisting of a groove formed into the inner surface of saidsleeve member but not passing completely through the side thereof, andvent means provided from the nonlinear groove to the outer surface ofsaid sleeve member. 10. The fluidic function generator set forth inclaim 9 wherein:

said axial groove having constant narrow width and depth dimensions toprovide a relatively high restriction to fluid flow therethrough, saidnonlinear groove having larger width and or depth dimensions than theaxial groove to provide a neg ligible restriction to fluid being ventedtherethrough.

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